444 



KNOV/LEDGE ♦ 



[Nov. 28, 1884. 



Fig. 1. — lUastrating the Geometrical Investigation of a Lunar Eclipse. 



and we must subtract a -iOOth part from the sun's semi- 

 diameter as seen from the earth to get that semi-diameter 

 as seen from the moon. 



With these elements our work is easy : — 

 We note first that at 10 h. 8 m. 53. -1, Greenwich mean 

 time, the earth's centre i.s 11' 24"-3 (the difference between 

 the declinations given above) south of the sun's centre. 

 Draw then a straight line A S B, Fig. 1, to represent a 

 parallel of declination through S the sun's centre, and with 

 any convenient length A // to represent 5', take S E square 

 to A B to represent 11' 24:"-3 : then E of course represents 

 the earth's centre at the time of conjunction of earth 

 and sun, in R.A. Now it will be obviously convenient to 

 keep the sun's centre at S throughout our investigation ; so 

 instead of having both the sun and earth moving, we note 

 that the earth gains on the sun, hourly, in R.A. 31' 56"-2, 

 and in declination 9' 55"-2 (we get these by taking 

 the difference between the hourly motions of the sun and 

 earth tabulated above). Now if A S B represented a de- 

 clination-parallel farther from the equator we ought to note 

 that a degree in R A along A B is less than a degree along 

 the equator ; but as a matter of fact the difference i.s not 

 more than 1 -250th part, and need not here trouble us. So, 

 first making a little scale of arc-minutes along A B, we set 

 off along SA a distance S D to represent 31' 56"-2, and 

 along DF square to S A take D F=ll' 24"-.3, and F = 

 9'5.5"-2;or DG = 2ri9"-5: then EG represents the 

 earth's motion from the sun during the hour following 

 conjunction in R.A. We draw LEGN to represent the 

 track of the earth's centre ; and S C sq\iare to L N, gives 

 the position of the earth's centre C at the time of nearest 



approach to the sun's, or the time of mid totality. E C 

 will be found to be about a tenth of E G the hourly 

 motion; that is, EC corresponds to about 6 min., and 

 central eclipse occurs therefore 6 min. before conjunction 

 in R.A. 



It will be convenient to take K a point one-third of E O 

 to the right of C, corresponding to the position of the 

 earth's centre at lOh., and then to mark in, carefully, the 

 hour and minute divisions corresponding to the earth's 

 motiou already determined.* 



Now describe round S a circle with radius 15' 59"'9 (1& 

 ■n-ill do well enough) to represent the sun's disc ; and round 

 C a circle with radius 59' 23" to represent the earth's ; thus 

 we have the relative position of the sun and earth, and 

 their relative dimensions, at the time of central totality, — 

 the observer being supposed to be at the moon's centre. 



We see that were it not for the refractive action of the 

 earth's atmosphere the sun ought to be entirely hidden ai 

 this time. This action brings the sun into view all round 

 (since C, the earth's centre, falls within the circle corre- 

 sponding to the sun's disc). But we note that more light 

 will be brought round the northern side of the earth than 



* AJso, we have, — 



sc : SE :: SD : GE 



or SC : Hi :: 32 : \/(32)-h- (lu)-, nearly enongh 

 (we have given approximate valnes to SE, S D, and F G). Or 

 SC = 1Hx32h-33J approximately. 



.2ix32x 

 " 3 



34x20 



168 



63 



= lOJ' very nearly. 



